# When a wire loop is rotated in a magnetic field, the direction of induced emf

$(a)\;\text{changes every 1/4 rotation} \\(b)\;\text{does not change} \\ (c)\;\text{change every 1/2 rotation} \\ (d)\;\text{changes every 1 rotation.}$

Flux of the magnetic field through the loop is $\phi =B \pi r^2 \cos wt$
Where $\theta=$ angle the normal makes with the portion of the loop in duced emf.
$\in = wB \pi r^2 \sin wt$
These is zero when $wt=n \pi$ ie
When $\theta=0, \pi,2 \pi....$ etc.
So, the induced emf changes direction every half rotation.
Hence c is the correct answer.

edited Sep 24, 2014